Engineering Transactions, 58, 1-2, pp. 15–74, 2010

The thermodynamical theory of elasto-viscoplasticity for description of nanocrystalline metals

Institute of Fundamental Technological Research Polish Academy of Sciences

The main objective of the present paper is the development of thermodynamical elastoviscoplastic
constitutive model describing the behaviour of nanocrystalline metals. Only fcc,
bcc and hcp metals will be covered in this description, because they are the classes of metals for
which systematic experimental observation data sets are available. Investigation of the deformation
mechanisms is important for understanding, controlling and optimizing of the mechanical
properties of nanocrystalline metals. Strengthening with grain size refinement in metals and
alloys, with an average grain size of 100 nm or larger, has been well characterized by the
Hall-Petch (H-P) relationship, where dislocation pile-up against grain boundaries, along with
other transgranular dislocations mechanisms, are the dominant strength-controlling processes.
When the average, and entire range of grain sizes is reduced to less than 100 nm, the dislocation
operation becomes increasingly more difficult and grain boundary-mediated processes
become increasingly more important. The principal short-range barrier, the Peierls-Nabarro
stress, is important for ultrafine crystalline bcc metals, whereas in ultrafine crystalline fcc and
hcp metals, forest dislocations are the primary short-range barriers at lower temperatures. Experimental
observations have shown that nanosized grains rotate during plastic deformation
and can coalesce along directions of shear, creating larger paths for dislocation movement.
The model is developed within the thermodynamic framework of the rate-type covariance
constitutive structure with a finite set of the internal state variables.
The thermodynamic restrictions have been satisfied and the rate-type constitutive equations
have been determined. Fracture criterion based on the evolution of the anisotropic intrinsic
microdamage is formulated. The fundamental features of the proposed constitutive theory
have been carefully discussed.
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